First, understand that every quote you get will be an "intro rate" which will be jacked up 10% or more per year. There's no use complaining, they'll just say the cost of claims went up at 4X the rate of inflation. In reality, they know most people won't go through the trouble of shopping. They make their profits on customers who've been with them 5+ years and haven't thought to shop.
The only way to win is to shop for new insurance every 2-4 years to get the intro rate again from a different company.
The downside is that you'll spend about 8 hours each time you shop. The upside is I save $300-500 (in a LCOL area) every time I shop. That's per year! And I shop every 3 years. Imagine how high my rates would be if I stuck with one company! Thousands of dollars are at stake with one of the easiest personal finance hacks imaginable.
To save time, develop a list of information requested by the first broker to offer you a quote. Then copy/paste this info for all subsequent brokers. Expect widely varying quotes.
Second piece of advice: A big emergency fund is a lot cheaper to maintain than low-deductible insurance. Ask for a $5k or $10k deductible on your homeowners policy and save hundreds of dollars per year for self-insuring. The ROI of this simple move is excellent. Plus, even if a hailstorm hits and you eat the entire cost of a new roof from your e-fund, you'll continue saving for years thereafter because you didn't file a claim.